Answer: The given statement is FALSE.
Step-by-step explanation: We are given to check whether the following statement is true or false :
"If the dimensions of a cylinder are doubled then its volume is quadrupled."
We know that
the volume of a cylinder with radius r units and height h units is given by

If the dimensions are doubled, then the new dimensions will be
R = 2r and H = 2h.
Therefore, the new volume will be

Thus, the volume of the new cylinder will be 8 times the original one, not quadrupled.
So, the given statement is FALSE.